John James: Created page with "{{Documentation subpage}} {{Wikipedia text|Template:Getprecision/doc|412746627}} NOTOC The '''Templat..."

2011-05-06T22:45:38Z

Created page with "{{Documentation subpage}} {{Wikipedia text|Template:Getprecision/doc|412746627}}  __NOTOC__ The '''Templat..."

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{{Wikipedia text|Template:Getprecision/doc|412746627}}

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The '''Template:Getprecision''' determines the precision (as a count of decimal digits) for any amount, large or negative, using
a fast algorithm. It can also handle a trailing decimal point (such
as "15." or "-41.") or trailing zeroes (such as "15.34000" having precision as 5 decimal digits).

===Examples===
Some examples:
:* <nowiki>{{getprecision| 0}}</nowiki> → {{getprecision| 0}}
:* <nowiki>{{getprecision| 1}}</nowiki> → {{getprecision| 1}}
:* <nowiki>{{getprecision| 22.45}}</nowiki> → {{getprecision| 22.45}}
:* <nowiki>{{getprecision| 22.12345}}</nowiki> → {{getprecision| 22.12345}}
:* <nowiki>{{getprecision| 22}}</nowiki> → {{getprecision| 22}}
:* <nowiki>{{getprecision| 22000}}</nowiki> → {{getprecision| 22000}}
:* <nowiki>{{getprecision| -15.275}}</nowiki> → {{getprecision| -15.275}}
:* <nowiki>{{getprecision| -15.2500}}</nowiki> → {{getprecision| -15.2500}}
:* <nowiki>{{Getprecision |23000222000111.432}}</nowiki> → {{Getprecision |23000222000111.432}}

:* <nowiki>{{getprecision| -15.123}}</nowiki> → {{getprecision| -15.123}}
:: <nowiki>{{precision| -15.123}}</nowiki> → {{precision| -15.123}} [ Getprecision handles negatives, but not {precision} ]

:* <nowiki>{{getprecision|0.09}}</nowiki> → {{getprecision|0.09}}
:* <nowiki>{{getprecision|0.88}}</nowiki> → {{getprecision|0.88}}
:* <nowiki>{{getprecision|880000}}</nowiki> → {{getprecision|880000}}
:* <nowiki>{{getprecision|90000000}}</nowiki> → {{getprecision|90000000}}

===Known bugs===
* For numbers in scientific notation, the precision is typically returned as too low by 1 decimal place. Example: <nowiki>{{getprecision |7.1234E+06}}</nowiki> → {{getprecision|7.1234E+06}} (should be precision as 4 decimal digits, not 3).
* Large numbers are limited to 11 trailing zeroes, so even larger numbers still report precision as being -11, such as 9 trillion: {{getprecision|9000000000000}} → {{getprecision|9000000000000}} (should be: -12).

===Technical notes===
*NOTE A1: This template determines the precision of decimals by counting the length of the numeric string (in a #switch comparing lengths of padded strings), then subtracting integer length, minus the decimal point, and minus 1 if negative. For integers, 1 place is subtracted for each trailing 0 on the integer. For fractions, any prior count is cleared x 0, then size is logarithm of denominator divided by log 10: (..prior...)*0 + floor(logn denom / logn 10 - .01) + 1.
*NOTE D2: The check, for whole integers, compares the amount versus appending "0" at the end: when the amount is a decimal, then the value is unchanged by appending 0 at the end: so 5.23 = 5.230 is true, whereas for whole integers, it would be: 5 = 50 as false, due to values becoming n*10 for integer n. So, for integer n, the check rejects: n = n0 as false; hence n is integer.
*NOTE M3: The magnitude of the integer portion is calculated by logarithm of the floor of absolute value (divided by [[natural logarithm]] of 10 to adjust for e=2.71828*), as: ln (floor( abs({{{1|-0.050067}}}) )+0.99 )/ln10 Function floor(x) trims the decimal part, to leave the whole count: 0-9 yield 0, 10-19 as 1, 1000-1999 as 3. The abs(x) avoids floor of negatives, floor(-0.1)= -1, hence using abs(x) ensures -0.1 floors to 0 not -1. Near zero, the +0.99 avoids invalid log of 0, but does not round-up any decimals, already floored as nnn.00. Complexity is 6 operations: floor of abs( {1} ) +0.99 then logn div logn10, then floor that logarithm ratio. Decimals -1 < x < 1 yield -1, avoiding log 0.001 = -3.
*NOTE N4: Nesting of if-else and nested templates is kept to a minimum, due to the MediaWiki 1.6 limit of 40 levels of if-logic for all nested templates used together. Template {ordomag} was omitted to avoid 2 more levels of nested templates. Template {Precision} had 8 levels, and this template was trimmed to only 5 levels.
*NOTE S5: The #switch is run with "x" prepended in front of the amount, otherwise a #switch will compare as numeric where "2" would match "2.0" even though "2" is length 1 so "x2" no longer matches with "x2.0" as non-numeric. The #switch will exit on the first match, so smaller lengths are compared first, to avoid extra comparisons for more rare, longer numeric strings up to 41 long.
*NOTE W6: The check for integers with whole end-zeroes uses typical n=n/10*10, for each power of 10, where whole millions match: <nowiki>{{#ifexpr: {1}=floor( {1}/1E6 )*1E6| }}</nowiki> Previously, {Precision} had tried to use "round" to detect end-zeroes but "round" loses precision at -5, so, n00000 round -5 differs from n00000 slightly, and comparisons to exact rounded amounts failed to match some numbers when 6 or more zeroes "n000000".
*NOTE Z7: The check on zero for any .00000 compares adding 1 to the amount, versus appending "1" at the end: if the amount is a decimal, then adding 1 will be larger than appending 1 at the end: 0.00 + 1 > 0.001, whereas for whole zero, it would be: 0+1 > 01 as false, due to the value being the same. So, for integer 0, the check rejects: 0+1 > 01 as false; hence whole 0 is integer.

===History===
*15Aug10 Created to get precision even if large or negative.
*15Aug10 Put NOTES comments to explain template coding.
*15Aug10 Put HISTORY comments to log major changes.
*18Aug10 Fixed to handle zero: 0 as 0, 0.000 as 3, etc.
*04Sep10 Fixed to handle decimals between 0~1 (by round 0).
*04Sep10 Updated NOTES to explain the check appending 0 or 1.
*03Jan11 Fix integer end-zeroes: 50 as -1, 500 as -2, 5000 -3.
*03Jan11 Omit {Order of Magnitude} for 2 levels less nesting.
*03Jan11 Omit {Str_len} for 8 fewer levels of 40-nest limit.
*03Jan11 Put "noinclude" around all inter-line HTML comments.
*03Jan11 Allow fraction "/": floor(logn denom/logn 10 -.01)+1.

===See also===
* [[Template:Precision]] - get precision of positive numbers

<includeonly>

[[Category:Mathematical function templates]]
[[Category:Templates with minimal expansion depth]]

</includeonly>

Template:Getprecision/doc - Revision history

John James: Created page with "{{Documentation subpage}} {{Wikipedia text|Template:Getprecision/doc|412746627}} __NOTOC__ The '''Templat..."

John James: Created page with "{{Documentation subpage}} {{Wikipedia text|Template:Getprecision/doc|412746627}} NOTOC The '''Templat..."